What is the maximum number of electrons in an atom that can have the quantum numbers n = 3, l = 2, m_l = 0?

• A. 2
• B. 6
• C. 4
• D. 1

Answer: (A)

Verified step by step guidance

1. Understand the meaning of each quantum number: \(n\) is the principal quantum number indicating the energy level or shell, \(l\) is the azimuthal (angular momentum) quantum number indicating the subshell or orbital shape, and \(m_l\) is the magnetic quantum number indicating the specific orbital within the subshell.
2. Given \(n = 3\) and \(l = 2\), identify the type of orbital: \(l = 2\) corresponds to the d subshell, which has five possible \(m_l\) values: \(-2, -1, 0, +1, +2\).
3. Since \(m_l = 0\) is specified, we are focusing on a single orbital within the d subshell (the one with magnetic quantum number zero).
4. Recall that each orbital can hold a maximum of 2 electrons, each with opposite spins (spin quantum number \(m_s = +\frac{1}{2}\) or \(-\frac{1}{2}\)).
5. Therefore, the maximum number of electrons that can have \(n=3\), \(l=2\), and \(m_l=0\) is 2.